Reduce to lowest terms: $- \dfrac{9}{4} \div - \dfrac{7}{4} = {?}$
Solution: Dividing by a fraction is the same as multiplying by the reciprocal of the fraction. The reciprocal of $- \dfrac{7}{4}$ is $- \dfrac{4}{7}$ Therefore: $ - \dfrac{9}{4} \div - \dfrac{7}{4} = - \dfrac{9}{4} \times - \dfrac{4}{7} $ $ \phantom{- \dfrac{9}{4} \times - \dfrac{4}{7}} = \dfrac{-9 \times -4}{4 \times 7} $ $ \phantom{- \dfrac{9}{4} \times - \dfrac{4}{7}} = \dfrac{36}{28} $ The numerator and denominator have a common divisor of $4$, so we can simplify: $ \dfrac{36}{28} = \dfrac{36 \div 4}{28 \div 4} = \dfrac{9}{7} $